20 October 2011, Volume 27 Issue 5
    

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  • Lv Tongling,Guo Junyi,Zhang Xin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 449-459.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    In this paper we consider a risk model
    with two correlated classes of insurance business. Asymptotic
    results for the deficit at ruin caused by different classes of
    insurance business are obtained. Explicit expression for the deficit
    at ruin caused by different classes of insurance business are given
    when the original claim size random variables are exponentially
    distributed. In addition we also give a brief discussion on the
    classical risk model perturbed by the Gamma process.

  • Fang Shizu,Zhang Chunmei,Zhao Peichen,Sun Xin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 460-472.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    In this paper, we consider the
    compound Markov binomial model proposed by Cossette et al.\,(2003).
    The defective renewal equations for the conditional and
    unconditional Gerber-Shiu discounted penalty function are obtained.
    The asymptotic expressions for the Gerber-Shiu discounted penalty
    function are then provided.

  • Dong Jiguo,Liu Guoxin
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 473-480.
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    In this paper, when the surplus
    has negative value, we allow the surplus process to continue. We
    consider, in the Markov-modulated risk model, the joint distribution
    of the supremum, the infimum and the number of zero of the surplus
    process before it leaves zero ultimately.

  • Yu Zhuoxi,Wang Dehui
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 481-496.
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    In this paper, the empirical likelihood
    method is extended to partial linear models with fixed designs under
    -dependent errors. We show that not the usual empirical
    likelihood but the blockwise empirical likelihood works in this
    situation, and the blockwise empirical log-likelihood ratio is
    asymptotically chi-squared distributed. A simulation study is
    reported to show its efficiency.

  • Chen Ying
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 497-510.
    Abstract ( ) Download PDF ( ) Knowledge map Save

    The ordinary ANOVA has been playing an
    important role in testing significant factors in experimental
    designs since it was developed. Especially for orthogonal designs,
    the ANOVA is almost the unique method of analyzing them. When the
    columns of an orthogonal array all are allocated by factors or
    interactions and it is impossible to do replicates, however, the
    ordinary ANOVA is no more applicable because there are no degrees of
    freedom left to estimate the error variance. This paper proposes a
    new test method for analyzing the orthogonal designs with only one
    replicate using complete orthogonal arrays. It is illustrated with
    some examples that the proposed method is practicable when the ANOVA
    is invalid. When there are a few empty columns of the orthogonal
    array used so that the ANOVA is applicable, the proposed method is
    more powerful than the ordinary ANOVA for some parameter
    configurations.

  • Li Xiaohu,Huang Yanyan,Zhao Xueyan
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 511-521.
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    The probability of success in a Binomial
    model is often viewed as a continuous random variable when
     needs to be considered. In this note, we study the
    mixed Binomial model with the probability of success having the
    Kumaraswamy distribution. Stochastic orders and dependence in this
    model are discussed; Further, the new models are employed to fit
    some real data sets, and the numerical results reveal that KB models
    perform better than Beta-Binomial model in some occasions.

  • Liu Yonghui
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 522-532.
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    Let and be two linear models with new observations. Through matrix rank
    method, we derive the necessary and sufficient conditions for the
    best linear unbiased predictor (BLUP) of the new observation under
    the model is also BLUP under the model
    . As applications, the conditions of equality of the
    BLUPs under two mixed linear models are also given.

  • Luo Zhongde,Yang Shanchao
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 533-542.
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    When we are using the local M-estimator with
    variable bandwidth to estimate, the collected data are not
    independent samples sometimes, but may be some mixing samples.
    Therefore, this paper discusses the strong consistency of
    M-estimator with variable bandwidth when the observational data are
    -mixing processes, and gives two theorems with some weaker
    assumptions.

  • Sun Guohong,Zhang Chunsheng,Ji Lanpeng
    CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST. 2011, 27(5): 543-560.
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    In this paper, we study the perturbed risk
    model with two classes of claims and a threshold dividend strategy.
    We assume that the two claim counting processes are, respectively,
    Poisson and renewal process with generalized Erlang(2) inter-claim
    times. Integro-differential equations and certain boundary
    conditions satisfied by the Gerber-Shiu penalty functions are
    derived in terms of matrices. Finally, we show that the closed form
    for the Gerber-Shiu penalty functions can be expressed by the
    Gerber-Shiu penalty functions without dividend payments and the
    matrix composed of two linearly independent solutions to the
    corresponding homogeneous integro-differential equations.